Cutting a hole in an angled surface
Maybe you should use boolean modyfier. 


Create an object that has the shape of the hole you want to create.

Add boolean modyfier to the object you want to cut a hole into.

Make sure that the operation type was set to difference. Choose object that you want to use as holecutter.





Slide the holecutter into the place where you want hole to be.

Apply the modyfier and remove the holecutter.

Hope you understood my bad english, but if this post helped then let me know by votng this answer up. Cheers! :)